Method and system for representing manufacturing and lithography information for IC routing

ABSTRACT

A mechanism to compress manufacturing awareness into a small representation and to enable the router to consult the representation without performing, or understanding, detailed process analysis, is disclosed.

BACKGROUND

With the advent of deep sub-wavelength lithography, the relationshipbetween width, spacing, and yield is more complex than it used to be.The conventional solution is obtained by running optical and etchingsimulation software to find the process window, and then simulatingprocess variations to find the expected yield. This may be acceptablefor defining process characteristics, but far too slow for a router thatmust make millions of width and spacing decisions to complete a singledesign.

In order to fabricate successfully, all lines and all spaces must printcorrectly. The spaces must print correctly, or else a short may occur.The lines must print correctly or an open may occur. Failure of the chipfabrication can occur for varied reasons. Three of the reasons arediscussed below. First, the dose or focus might be off enough so thatthe line or space does not print properly. This may be referred to as an‘optical’ problem, or a lithography problem. Second, a stray particlecan land on the mask or wafer, perhaps breaking a line or causing ashort. This can be referred to as a ‘particle’ problem. Third, a via canfail to work correctly, due to variety of reasons. This may be referredto as a ‘via’ problem. These challenges are described in more detail inthe following paragraphs.

The particle problem is well understood. Particle size distribution canbe measured for a given set of fabrication constraints. For example,FIG. 1 is a representation of a particle size distribution graph todetermine the number of particles of a particular size that may beavailable to cause a failure. The graph shows that as the particle sizedecreases the number of particles in a square centimeter increases. Thusthe odds of failure are reduced if the width or spacing is greater thanthe smaller particle sizes. However, in the absence of detailed datasome particle size distribution can be assumed (1/x³ is typical).

A ‘critical area’ can be measured for any size particle—this criticalarea is the area of the portion of the layout where the chip wouldmalfunction if the center of a particle of the specified size landed inthis area. The particle size distribution and critical area determinethe yield from this effect. In general, the details of this model havenot mattered much to routers since the curve is so steep that thesolution to date has been to evenly distribute any remaining space.

The optical, or lithography, problem in which the dose (i.e., exposure)and focus may be skewed, is where the recent complexities occur. Here abigger spacing is not always better, and may be considerably worse. Infact some dimensions, even though larger than the minimum, may not bepermitted at all. These “not-permitted” dimensions may be referred to as“forbidden pitches,” and result from the sophisticated optical tricksneeded to print these sizes at all. For example, lithography may beoptimized to print the narrowest lines and spaces. Larger spaces willthen work less well, until the spacing is large enough to allow assistfeatures (may be referred as scattering bars) to be inserted. In somecases the process window at the intermediate spacing is so small thereis virtually no chance of both the space and the lines printingcorrectly, this is a forbidden pitch.

One prior solution is referred to as ‘design rules’. These rules may bevery simple and binary in nature. Any solution that meets the rules isacceptable (and all solutions are equally acceptable), and any solutionsthat does not meet the rules is forbidden (and all such solutions areequally forbidden). The rules are simple, consisting of, at most, a listof spacings according to wire width, and often just a single minimumwidth and spacing. For example, a common routing design rule is to routea wire no closer to an object than some specified minimum spacing(typically roughly equal to the width of the wire) so that they willhave enough space to function properly.

Another prior solution is referred to as ‘scripts’. Scripts are commandsequences that tell the router what to do. For example, the scripts mayinstruct the router to first double all vias wherever there is enoughspace, and then route the remaining wires. These scripts are intended bythe user to result in designs with increased yield. However, this is notalways the case.

The drawback to both previous solutions is that they do not describe thereal manufacturing system very well. In practice, different spacings andwidths have different degrees of manufacturability. Second, because ofthe binary nature of the rules, there is no guidance once the rules aremet. That is, each scenario that meets rules is treated equal to theother scenarios that meet the rules, when that may not be the case.Exact minimum spacing, twice this spacing, and so on, are all exactly asgood to the router. So the router has no reason to pick oneconfiguration over another.

Some more specific example problems include:

Existing routers cannot include considerations of lithography, particleyield, and via problems simultaneously.

Existing routers cannot make an intelligent choice among manyalternatives, since all are exactly equal under the older concept ofdesign rules.

Existing routers cannot obey the idea of ‘forbidden pitch’, wherecertain spacings are not permitted even though a smaller spacing isacceptable or fits within the design rules.

Existing routers cannot make an intelligent tradeoff between extra viasand increased critical area, so it must follow simple strategies such asdoubling all vias, then increasing spacing, even though this may not beoptimum and in fact hurt the overall yield. For example, FIG. 2illustrates single, double and triple vias. Single via 212 is surroundedby metal 210. Double vias 222 and 224 is surrounded by metal 220 andtriple vias 232, 234, 236 are surrounded by metal 230. Adjacent to thevia objects is object 240. When a via is doubled or tripled theprobability of the via working increases, however, the critical areabetween the via(s) and the adjacent object increases as well. That is,as the via yield is increased, the line printing yield may decrease orthe critical area may be large enough for a particle failure. Forexample, single via 212 has a critical area 218. However critical area228 associated with double vias 222 and 224 is larger than critical area218, and thus the line printing may have a lower yield due to particleproblems than single via 218. Similarly, critical area 238 associatedwith triple vias 232, 234, and 236 is larger still and may have a loweryield than a double via or single via.

Existing routers cannot maximize yield, which is what the user reallywants. Instead it simply tries to minimize area, which may or may notlead to the maximum yield design. In particular, existing routers maynever consider non-minimum sized designs, even though they may haveenough increased yield to more than compensate for their larger size.

Existing router and extractor estimates of parasitics and critical areasdo not take into account how the real manufactured silicon will looksince it is too time consuming to do so, even though this informationcan be calculated.

SUMMARY

A mechanism to compress manufacturing awareness into a smallrepresentation and to enable the router to consult the representationwithout performing, or understanding, detailed process analysis, isdisclosed. A mechanism to compress manufacturing awareness into a routeraware representation includes obtaining the fabrication constraints,obtaining the space and wire data, obtaining the particle data,obtaining the via data, and storing the data into tables for the routerto access.

A method for routing an IC may include extracting a first set ofinformation, extracting a second set of information, and creatingrouting alternatives based on the first set and second set ofinformation.

A system for IC routing may include a set of particle informationtables, a set of via information tables, and a routing engine.

A method for compressing manufacturing awareness into a routerrepresentation for integrated circuit routing includes obtaining a setof fabrication parameters, obtaining particle data, obtaining via data,normalizing the particle and via data, and storing the data in tablesfor the router to access while making routing decisions.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 represents an example particle data chart.

FIG. 2 represents example single, double and triple vias.

FIG. 3A represents an example design used to generate wire table data.

FIG. 3B represents an example design used to generate space table data.

FIG. 3C represents a flow diagram that illustrates the derivationprocess for lithography table information.

FIG. 4 represents example across and along measurements.

FIG. 5 represents example via data.

FIG. 6A represents a flow diagram that illustrates an embodiment of therouter contemporaneously considering sets of information.

FIG. 6B represents a flow diagram that illustrates an embodiment of therouter comparing alternative routings.

DETAILED DESCRIPTION

A way to compress manufacturing awareness into a small representationthat the router may consult without the need to perform (or understand)detailed process analysis is discussed and includes a way for routersand extractors to take lithographic constraints into account duringtheir estimates of parasitics.

In one embodiment, three sets of tables provide this awareness. One setof tables describes the problem of printing spaces and lines, a secondset of tables details the problems of particles, and the third set oftables details the problems of vias. The first set of tables tell therouter the likelihood of optical problems. In the explanation below,vertical lines are used, but other lines may be used as well. Also inthis example, parallel lines dominate the yield for machine routed data.

The first set of tables may include two tables. A first table includesline printing information. A second table includes space printinginformation. The optical line printing table, in some embodiments, maybe indexed by space width, wire width, space width, wire width, spacewidth (space-width-space-width-space, or SWSWS). The optical spaceprinting table, in some embodiments, may be indexed by wire width, spacewidth, wire width, space width, and wire width.(width-space-width-space-width, or WSWSW). In some embodiment, eachwidth and spacing may assume 10 values, that is 100,000 entries for eachof the two tables. This structure may be referred as a five-dimensionaltable with each width considered a dimension. In other embodiments, athree-dimensional table structure may be implemented with an indexing ofSWS and WSW with fewer entries per table.

The wire and space printing information may be obtained by process 350in FIG. 3C. In process action 352 a design is created. An example wireprinting design 300 is shown in FIG. 3A. An example space printingdesign in shown in FIG. 3B. In process action 354, the design issimulated with a process model using the fabrication parameter. Processaction 356 computes the process window and stores it in the table interms of focus and dose. Process 358 computes the odds that theparticular design works using more detailed (but time consuming) methodssuch as optical simulation and Monte Carlo analysis. Process action 360determines if the design will work. If the design works, process action362 computes the center and size of the sweet spot. In some embodiments,this information may be stored in an application data table for use bythe router, other embodiments do not use this information at all. If thedesign does not work, or after the center and sweet spot are computed,process action 364 determines if there are more designs to test. Ifthere are more designs to test, process action 365 selects the nextdesign and returns process 350 to process action 352. If there are nomore designs to test, process 350 stops.

The plurality of designs may be created by altering the widths of eachof the spaces and wires in the example designs, such as those shown inFIGS. 3A and 3B. The quantity of designs tested may vary. It may takemore time to design and test more examples but the reward is moreaccurate data for the router. Some embodiments may require more accuratedata and may utilize 10 values for each of the width dimensions creating100,000 designs for wire data and 100,000 designs for spacing data,whereas some embodiments may require faster results and utilize fewerdimensions or fewer values for each dimension creating fewer designs.

A more quantitative generalization of forbidden pitch can be representedin the wire and space tables. A completely forbidden pitch can berepresented in this format as a zero-sized process window. Also, the badpitches can depend on the width of the wires on either side, as isdesired.

Some embodiments may use application information associated with theline and space printing tables. This information may include, forexample, the center of the sweet spot of the process window in terms offocus and dose as calculated in process action 362 in FIG. 3C, and theexpected displacement of the edge (as manufactured) from where it wasdrawn. Uses of this application information are explained later.

The second set of tables details the problems of particles and criticalarea calculations. In this set there may be two tables. A first tablemay describe the probability of a particle causing an undesirable opencircuit. A second table may describe the probability of a particlecausing a short circuit. The information in the tables indicates thenumber of particles per square centimeter that are likely to beavailable in a clean room that could cause a failure per a certain sizeof critical area. That is, critical area is based on the distribution ofparticle sizes and the probability of the particle landing on the space.

The critical area is computed between every piece of neighboringmaterial. For illustration, FIG. 2 shows the computation for the metalassociated with via(s), but in fact all materials are considered. Forexample, critical area 218 in FIG. 2 has a certain probability offailure due to open circuits and a certain probability of failure due toshort circuits. Critical areas 228 and 238 in FIG. 2 have higherprobability of failure than critical area 218 because there is a longerspace that has to be concerned about a landing particle.

The third set of tables reflects the overlap of cuts and the odds that avia instance fails. An expression to represent this relationship may berel=ƒ(number of cuts, overlaps). That is, the critical area failureprobability is a function of both the number of cuts, or number of vias,and the metal overlap of the vias. The number of vias may be single,double, triple or even more. Overlap of vias involves the width of themetal surrounding the set of vias. The width of metal surrounding thevia may be referred to as the across and the along. An example of thesemeasurements is shown in FIG. 4. Along 405 is the measurement from theend of the via to the short side of the metal. Across 410 is themeasurement from the end of the via to the long side of the metal. Thewidth of these two measurements impacts the probability of failure dueto misalignment, overetching, and other possible fabrication problems.This data is layer dependent. That is, each layer may have differingcharacteristics such as thickness or material, and thus each layer mayhave a differing contribution to failure probabilities. Consequently,each layer has its own via data. Further, there may be a single, double,triple, or more vias in each layer, and since that via may be cuttingthrough to the layer above or to the layer below there may be two set ofinformation per via. In some embodiments, there may be six tables ofdata for each layer—a table for odds of a failure of a single via to thelayer below, a table for odds of a failure of a single via to the layerabove, a table for odds of failure of a double via for the layer below,a table for odds of failure of a double via to the layer above, a tablefor odds of failure of a triple via to the layer below, and a table forodds of failure of a triple via to the layer above. In one embodiment,the triple, quadruple (or more) vias are all assumed to fail at thetriple via rate, since due to all the redundancy, all such vias are veryreliable, and distinguishing between them will not significantly impactthe results. Example via data is shown in FIG. 5. The chart shows acrosswidth versus the along width. Each grid space details the odds that aparticular across value and a particular along value pair will have afailure. In some embodiments, there may be only one number in the grid,that is, each grid position is assumed to have the same odds of failure.

Each of the tables may be calculated in similar units so they can easilybe combined into a total manufacturing yield analysis, including eachtype of failures as appropriate. In some embodiments, the estimates arerealistic failure rates, that are close to actual fabrication figures.In this case, cost may be calculated as cost=−log(failure rate), andthen a real yield can be estimated. However, this is not necessary,since in general the router is comparing configurations. In anembodiment where the estimates are not realistic failure rates, theentries may be treated as costs, and only their relative magnitude issignificant. Using cost values simplifies calculations for the routerbecause the router is already accustomed to evaluating costs offabrication. Thus, translating the failure rates into costs places thedata into terms the router understands and can manipulate. FIG. 6A is anillustration of an example router process 600. In process action 602 therouter extracts a first set of information from the tables. In processaction 604 the router extracts a second set of information from thetables. In some embodiments, the first set and second set of informationcan include any two of particle information, via information, andlithography information. In other embodiments, three sets of informationmay be used taking into consideration particle, via, and lithographyinformation contemporaneously in routing decisions. In process action606 the router creates alternative routings based on the two sets ofinformation. In some embodiments the designer weighs the pros and consof each alternative routing and chooses the most suitable one for hisneeds. In some other embodiments the router may be programmed to selectthe most suitable routing.

With this information, the router can make intelligent choices in usingextra space for extra width, for extra spacing, or for a combination. Itcan also choose intelligently between an extra via and wider spacing.For example, the router may have some extra room and needs to decide howto use it. The goal is to have the vias, the spaces, and the wire widthswork. For example, let the total amount of room available be R. Then therouter can select spaces and wire widths (e.g., S1, W2 and S2) such thatS1+W2+S2=R, where S1=−log(failure rate of S1), S2=−log(failure rate ofS2) and W2=−log(failure rate of W2). Process 625 shown in FIG. 6Billustrates the embodiment of the router selecting between alternatives.In process action 630, the router calculates the table values of thealternatives. In some embodiments the table values are the odds offailure or failure rate. In other embodiments the table values are“costs” calculated by taking the −log of the failure rate. In someembodiments the costs can be weighted. In process action 635 thealternatives are compared. In process action 640 the router selects oneof the alternatives. In some embodiments, the router may choose analternative based on yield alone. In some embodiments, the router maychoose an alternative based on yield and cost or based on yield, costand timing.

In a similar way, the router can now decide in an intelligent way aboutthe relative merits of the two configurations. The two spaces (S1, S2)must print, the wire (W2) must print, and at least one of the two vias(the original and the extra via) must work. The calculation is slightlymore complex since the length of wire at the various spacings changes aswell, but it still boils down to minimizing the (weighted) sum ofvarious failure probabilities. In particular, note that if putting thewire in the center results in two forbidden pitches, then the router maymove the wire to one side or the other.

The following example is an embodiment of when the router can use theapplication information from the tables. In a real chip, the spaces andthe wire share a single random focus and dose since they are very closetogether. Theoretically it is possible for the first space to printcorrectly 50% of the time, and the second space to print correctly 50%of the time, but for there to be no conditions under which they bothprint correctly, so the yield is 0 rather than 50%. Once the processregions are obtained, they can be checked for this scenario. Using theapplication table entries of center of the sweet spot and size of thesweet spot for both spaces and the lines, the router can look at theoverlap to check for compatibility.

Another application entry is a field containing ‘edge displacements asprinted on the silicon’ entry. The router and/or extractor may use thisto modify the electrical equivalent widths of the wires and then computean ‘optically correct extraction’ for very little additional cost. Itmay also lead to a much more accurate critical area calculation. In someembodiments a line/space based model may be used, where each edgedisplacement can be computed twice, since each edge is one edge of aspace and one edge of a line. In some embodiments a program can use theaverage of the two computed displacements. In other embodiments, thederivatives of the edge placement may be listed with changes.

In some embodiments, the lithographic tables can be restated in terms oflithographic effects on edges, rather than on lines or spaces. Thiswould require fewer tables, but the complexity of the calculation of theodds that a given line or space prints correctly would increase, sinceeach line or space has two edges.

In some embodiments, extra tables may be included for use in specialcircumstances (such as local density or orientation). These tables canbe used to make adjustments for particular circumstances.

In some embodiments, the data can also be developed using functions,rather than tabulated values if a set of suitable functions can befound. Alternatively, the tables could contain the joint probability ofsuccess, at least for a wire and adjoining spaces, instead of specifyinga process window and having the router compute this. Also, various otherformats can be used to express this idea.

In some embodiments, when computing the odds of failure, the idea thatprinting ‘fails’ can be determined in many ways. For example, printingfailure could be when the line becomes and open (or the space actuallyshorts), or could be when the line or space goes out of geometricaltolerance, or some other criteria.

In some embodiments, instead of, or in addition to process windows, thetables could contain the nominal result and sensitivities with respectto the relevant variables, such as dose and focus. For example, aprocess window might state that the wire width will be acceptableprovided the dose is between 18 and 22 mJ/cm². The sensitivity basedversion might say that the resulting wire width=100 nm+10 nmcm²/mJ*(dose−20 mJ/cm²) between. Then the user (or program) can computethe range of acceptable doses based on their knowledge of the acceptablewidth for the wire.

The method allows the router to include considerations of bothlithography and particle yield problems, provides enough information sothe router can intelligently select among alternatives, and allows theexpression of ‘forbidden pitch’, where a particular pitch is not allowedeven though a smaller pitch is OK.

The method further allows the router to make an intelligent tradeoffbetween extra vias and increased critical area. The goal of the routeris to maximize yield, a truer indication of what the user wants, ratherthan just minimizing area. This may potentially result in non-minimumsized designs not currently considered by existing routers.

The extraction of parasitics and critical areas to take into account howthe real manufactured silicon will look, at least to first order,without the need to do time consuming simulations, can be performed withthis method, with use of tables to convey essential lithographicinformation to a router. This allows a router to use probability ofcorrect construction, rather than minimum width and spacing.

Therefore, the router makes decisions with a goal of maximize yield,taking into consideration any two or three of lithography, particle, andvia constraints simultaneously. The router also has the ability to tradeoff among the yield losses induced by via failure, lithography failure,and particle failure.

What is claimed is:
 1. A method of routing an electronic circuit designof an electronic circuit, the method comprising: extracting, by using arouter or an extractor, a first set of information for the electroniccircuit design from a first set of data structures, wherein the firstset of information is to be used by the router for routing theelectronic circuit design; extracting, by using the router or theextractor, a second set of information for the electronic circuit designfrom a second set of data structures, wherein the second set ofinformation is to be used by the router for routing the electroniccircuit design, wherein the first set of information comprises particleinformation, and the second set of information is selected from a groupcomprising via information and lithography information; displaying thefirst set of information or the second set of information on a displayapparatus or storing the first set of information or the second set ofinformation on a storage device or a tangible computer readable medium;and creating, by using a processor, a first routing of the electroniccircuit design based on the first and second sets of information.
 2. Themethod of claim 1, further comprising: creating a second routing of theelectronic circuit design based on the contemporaneous consideration ofthe first set of information and the second set of information;comparing the first routing and the second routing of the electroniccircuit design to determine whether the first routing or the secondrouting performs better; and selecting one of the first routing or thesecond routing based on the comparison.
 3. The method of claim 2,wherein comparing the first and second routing comprises: summing afirst probability of failure data associated with the first routing;summing a second probability of failure data associated with the secondrouting; and comparing the sums.
 4. The method of claim 2, whereincomparing the first and second routing comprises: summing first costdata associated with first routing; summing second cost data associatedwith the second routing; and comparing the sums.
 5. The method of claim1, wherein the act of creating the first routing is performed without aneed for performing analysis of or simulating a fabrication processmodel.
 6. The method of claim 2, wherein the comparison is based onyield or cost.
 7. The method of claim 1, wherein the first set ofinformation or the second set of information comprises a jointprobability of success of at least two of the particle information, thevia information, and the lithography information for fabricating acircuit feature of the electronic circuit.
 8. The method of claim 1,wherein the particle information includes information regardingparticles that are identified, during manufacturing of the electroniccircuit, at one or more locations so as to cause an open circuit or ashort circuit.
 9. The method of claim 1, wherein the via informationincludes information regarding single vias, double vias, and triple viasto and from each layer.
 10. The method of claim 1, wherein the firstrouting comprises an initial routing of the electronic circuit design.11. The method of claim 10, wherein creating the first and secondroutings includes making trade-offs between increasing vias andincreasing critical area.
 12. The method of claim 10, wherein the act ofcreating the first routing by the router comprises optimizing yield offabrication of the electronic circuit.
 13. The method of claim 7,wherein the lithography information includes forbidden pitch, forbiddenpitch being an instance in which chances of both a set of lines and aset of spaces printing properly approximates zero even though the set ofspaces is larger than a minimum space value.
 14. The method of claim 7,wherein the lithography information includes information regarding aplurality of wire printing scenarios and information regarding aplurality of space printing scenarios.
 15. The method of claim 1,wherein the first and second set of tables comprise probability offailure information.
 16. The method of claim 1, wherein the first and,second set of tables comprise cost information.
 17. The method of claim1, further comprising: extracting a third set of information; andcreating the first routing based on the first, second, and the thirdsets of information.
 18. A system for routing an electronic circuitdesign, the system comprising: means for extracting, by using a routeror an extractor, a first set of information for the electronic circuitdesign from a first set of data structures, wherein the first set ofinformation is to be used by the router for routing the electroniccircuit design; means for extracting, by using the router or theextractor, a second set of information for the electronic circuit designfrom a second set of data structures, wherein the second set ofinformation is to be used by the router for routing the electroniccircuit design, wherein the first set of information comprises particleinformation, and the second set of information is selected from a groupcomprising via information and lithography information; means forcreating a first routing of the electronic circuit design based on thefirst and second sets of information, wherein the means for creatingcomprises a processor; and a display apparatus configured for displayingthe first set of information or a second set of information or a storagedevice or a tangible computer readable medium configured for storing thefirst set of information or the second set of information.
 19. Thesystem of claim 18, further comprising: means for creating a secondrouting of the electronic circuit design based on the contemporaneousconsideration of the first set of information and the second set ofinformation; means for comparing the first routing and the secondrouting of the electronic circuit design to determine whether the firstrouting or the second routing performs better; and means for selectingone of the first routing or the second routing based on the comparison.20. The system of claim 19, wherein the means for comparing the firstand second routing comprises: means for summing a first probability offailure data associated with the first routing; means for summing asecond probability of failure data associated with the second routing;and means for comparing the sums.
 21. The system of claim 19, whereinthe means for comparing the first and second routing comprises: meansfor summing first cost data associated with first routing; means forsumming second cost data associated with the second routing; and meansfor comparing the sums.
 22. A computer program product that includes acomputer-readable volatile or non-volatile medium having a sequence ofinstructions which, when executed by a processor, causes the processorto execute a process for routing an electronic circuit design,comprising: extracting, by using a router or an extractor, a first setof information for the electronic circuit design from a first set ofdata structures, wherein the first set of information is to be used bythe router for routing the electronic circuit design; extracting, byusing the router or the extractor, a second set of information for theelectronic circuit design from a second set of data structures, whereinthe second set of information is to be used by the router for optimizingthe yield of the fabrication of the electronic circuit design, whereinthe first set of information comprises particle information, and thesecond set of information is selected from a group comprising viainformation and lithography information; displaying the first set ofinformation or the second set of information on a display apparatus orstoring the first set of information or the second set of information ona storage device or a tangible computer readable medium; and creating,by using a processor, a first routing of the electronic circuit designbased on the first and second sets of information.
 23. The computerprogram product of claim 22, further comprising: creating a secondrouting of the electronic circuit design based on the contemporaneousconsideration of the first set of information and the second set ofinformation; comparing the first routing and the second routing of theelectronic circuit design to determine whether the first routing or thesecond routing performs better; and selecting one of the first routingor the second routing based on the comparison.
 24. The computer programproduct of claim 23, wherein comparing the first and second routingcomprises: summing a first probability of failure data associated withthe first routing; summing a second probability of failure dataassociated with the second routing; and comparing the sums.
 25. Thecomputer program product of claim 23, wherein comparing the first andsecond routing comprises: summing first cost data associated with firstrouting; summing second cost data associated with the second routing;and comparing the sums.